Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 18, Problem 98P
(a)
To determine
The expression for
(b)
To determine
The time take by car tire to go flat.
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The free energy is defined as follows:
av (k₂1)³2
5/2
F = Nk, Tin
N
Here, Nis the number of particles of gas, Vis the volume of the gas, I is the
k₂
temperature of the gas, is the Boltzmann constant, and is the constant.
What is the internal energy of the gas?
(a) - NKT
(b)-NK, I
(c) Nk T
(d) ——— Nk¸T
Compute the density in units of of an ideal gas under the following conditions:
a) At and Torr pressure (1 Torr = 1mm Hg) this is called loschmidt number.
b) In a vacuum of Torr at room temperature . This number is useful one for the experimentalist to know by heart. (10^-3 Torr = 1 micron)
Calculate the average speed, ī of molecules in a gas using the Maxwell-Boltzmann distribution function.
You will need the following Gaussian integral relation,
1
ve-au du
%3D
2a²
Chapter 18 Solutions
Physics for Scientists and Engineers
Ch. 18 - Prob. 1PCh. 18 - Prob. 2PCh. 18 - Prob. 3PCh. 18 - Prob. 4PCh. 18 - Prob. 5PCh. 18 - Prob. 6PCh. 18 - Prob. 7PCh. 18 - Prob. 8PCh. 18 - Prob. 9PCh. 18 - Prob. 10P
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- 1. (1) Use the Maxwell speed distribution function F(v) for an ideal-gas particle to derive the most probable speed v*, average speed u = (v), root-mean-square speed vyms = V(u2) = 3K5", where mis the mass of the ideal-gas particle, kg is the Boltzmann m constant, and T is the temperature. (1I) prove that Vrms >i >v*. (III) Rewrite the Maxwell speed distribution function F(v) as a function related to and v*, i.e., F (, v*). How much percentage do ideal-gas particles distribute at v*±(0.5% v*), v±(0.5% v*), and vms±(0.5% v*), respectively? (IV) Use the Maxwell velocity distribution function f (T) to determine the average velocity of the ideal gas (ī).arrow_forwardProblem 6: There are lots of examples of ideal gases in the universe, and they exist in many different conditions. In this problem we will examine what the temperature of these various phenomena are. Part (a) Give an expression for the temperature of an ideal gas in terms of pressure P, particle density per unit volume ρ, and fundamental constants. T = P/( ρ kB ) Part (b) Near the surface of Venus, its atmosphere has a pressure fv= 96 times the pressure of Earth's atmosphere, and a particle density of around ρv = 0.92 × 1027 m-3. What is the temperature of Venus' atmosphere (in C) near the surface? Part (c) The Orion nebula is one of the brightest diffuse nebulae in the sky (look for it in the winter, just below the three bright stars in Orion's belt). It is a very complicated mess of gas, dust, young star systems, and brown dwarfs, but let's estimate its temperature if we assume it is a uniform ideal gas. Assume it is a sphere of radius r = 5.8 × 1015 m (around 6 light years)…arrow_forwardConsider 1 mole of a van der Waals gas. (i) Derive the expressions for the pressure, pc, temperature, Tc, and volume, Vc, in the critical point of a van der Waals gas in terms of parameters a, b and R. Derive the vdw equation in reduced coordinates p =,= 7, V = V/ (ii) (iii) Find how many times the gas temperature exceeds its critical temperature if the gas pressure is 4 times as high as critical pressure and the volume of gas is equal to twice the critical volume.arrow_forward
- For a one-dimensional problem of a gas medium confined between two parallel plates, determine the direct exchange factor gig; (i.e., per unit area), where medium zone i is an infinitely large slab of thickness Az (located between z, sz s zi + Az), and j is another medium zone (located at z, sz s 2; + Az).arrow_forwardIf the volumetric expansion coefficient of an ideal gas is (1/T) and the compression coefficient (1/p), prove the equation of state for an ideal gas pv = nRT if (v, T) v = varrow_forwardSend me solution asaparrow_forward
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